Binary Search Tree Iterator
Difficulty: Medium
Category: DSA
Topics: Stack, Tree, Design, Binary Search Tree, Binary Tree, Iterator
Asked at: Facebook, ByteDance, Microsoft, Bloomberg, Google, Oracle, Amazon, Apple, Adobe
Implement the `BSTIterator` class that represents an iterator over the **in-order traversal** of a binary search tree (BST):
- `BSTIterator(TreeNode root)` Initializes an object of the `BSTIterator` class. The `root` of the BST is given as part of the constructor. The pointer should be initialized to a non-existent number smaller than any element in the BST.
- `boolean hasNext()` Returns `true` if there exists a number in the traversal to the right of the pointer, otherwise returns `false`.
- `int next()` Moves the pointer to the right, then returns the number at the pointer.
Notice that by initializing the pointer to a non-existent smallest number, the first call to `next()` will return the smallest element in the BST.
You may assume that `next()` calls will always be valid. That is, there will be at least a next number in the in-order traversal when `next()` is called.
**Example 1:**
**Input**
["BSTIterator", "next", "next", "hasNext", "next", "hasNext", "next", "hasNext", "next", "hasNext"]
[[[7, 3, 15, null, null, 9, 20]], [], [], [], [], [], [], [], [], []]
**Output**
[null, 3, 7, true, 9, true, 15, true, 20, false]
**Explanation**
BSTIterator bSTIterator = new BSTIterator([7, 3, 15, null, null, 9, 20]);
bSTIterator.next(); // return 3
bSTIterator.next(); // return 7
bSTIterator.hasNext(); // return True
bSTIterator.next(); // return 9
bSTIterator.hasNext(); // return True
bSTIterator.next(); // return 15
bSTIterator.hasNext(); // return True
bSTIterator.next(); // return 20
bSTIterator.hasNext(); // return False
```
**Constraints:**
- The number of nodes in the tree is in the range `[1, 105]`.
- `0 <= Node.val <= 106`
- At most `105` calls will be made to `hasNext`, and `next`.
**Follow up:**
- Could you implement `next()` and `hasNext()` to run in average `O(1)` time and use `O(h)` memory, where `h` is the height of the tree?